Vida has just won a jackpot that will pay her $10,000 now, $10,000 in one year, and $10,000 in 2 years. What is the present value of this jackpot at the continuously discounted rate of 9%?
A) $27,515
B) $28,345
C) $24,516
D) $27,492

Question

Quizplus · Accepted Answer

The present value (PV) of a future amount of money is calculated using the formula PV = FV / e^(rt), where FV is the future value, r is the continuous discount rate, and t is the time in years. For Vida's jackpot, we calculate the present value of each payment separately and then sum them up. 1. The first payment of $10,000 is already in present value since it's paid now.2. The second payment's present value: $10,000 / e^(0.09*1) = $10,000 / e^0.09 ≈ $9,168.243. The third payment's present value: $10,000 / e^(0.09*2) = $10,000 / e^0.18 ≈ $8,323.71Adding these up: $10,000 + $9,168.24 + $8,323.71 = $27,492Therefore, the present value of the jackpot at the continuously discounted rate of 9% is approximately $27,492.

Vida Has Just Won a Jackpot That Will Pay Her